Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class Task3 {

    public static void main(String[] args) throws Exception {



        new Task3().solve();

    }

    //ArrayList<Integer>[] g;

    int mod = 1000000007;

    PrintWriter out;

    int n;
    int m;

    ArrayList<Integer>[] g;
    ArrayList<Integer>[] a;

    void solve() throws IOException {

        //Reader in = new Reader("in.txt");
        //out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        Reader in = new Reader();
        out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );

        //BufferedReader br = new BufferedReader( new FileReader("in.txt") );
        //BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );

        int n = in.nextInt();
        int m = in.nextInt();
        int q = in.nextInt();

        g = new ArrayList[n];
        a = new ArrayList[n];

        for (int i = 0; i <n; i++) {
            g[i] = new ArrayList<>();
            a[i] = new ArrayList<>();
        }

        for (int i = 0; i < n - 1; i++) {

            int x = in.nextInt()-1;
            int y = in.nextInt()-1;

            g[x].add(y);
            g[y].add(x);
        }

        for (int i = 0; i < m; i++) {

            int x = in.nextInt()-1;
            a[x].add(i+1);
        }

        while (1 << lg <= n)
            lg++;

        dfs(0, 0);

        for (int i = 0; i < q; i++) {

            int x = in.nextInt()-1;
            int y = in.nextInt()-1;
            int c = in.nextInt();

            int lca = lca(x, y);

            ArrayList<Integer> res1 = q(x, lca);
            ArrayList<Integer> res2 = q(y, lca);

            ArrayList res = merge(res1, res2);

            out.print( Math.min(res.size(), c)+" ");

            for (int j = 0; j < Math.min(res.size(), c); j++) {
                out.print(res.get(j)+" ");
            }
            out.println();
        }

        out.flush();
        out.close();
    }

    int[] tin = new int[100000];
    int[] tout = new int[100000];
    int time = 0;
    int lg = 1;

    int[][] dp = new int[20][100000];
    ArrayList<Integer>[][] val = new ArrayList[20][100000];

    ArrayList q(int v, int b) {



        ArrayList<Integer> res = new ArrayList<>();

        if (v == b) {

            return a[b];

        }

        for (int i = lg; i >= 0; i--) {

            if (!upper(dp[i][v], b)) {

                res = merge(res, val[i][v]);
                v = dp[i][v];
            }
        }

        res = merge(res, val[0][v]);

        return res;
    }

    int lca(int a, int b) {

        if (upper(a, b))
            return a;

        if (upper(b, a))
            return b;

        for (int i = lg; i >= 0; i--)
            if (!upper(dp[i][a], b))
                a = dp[i][a];

        return dp[0][a];
    }

    boolean upper(int a, int b) {

        return tin[a] <= tin[b] && tout[a] >= tout[b];
    }

    void dfs(int v, int p) {

        tin[v] = time++;
        dp[0][v] = p;
        val[0][v] = new ArrayList<>();
        val[0][v] = merge(a[v], a[p]);

        for (int i = 1; i <= lg; i++) {
            dp[i][v] = dp[i-1][dp[i-1][v]];
            val[i][v] = merge(val[i-1][v], val[i-1][dp[i-1][v]]);
        }

        for (int u : g[v])
            if (u != p)
                dfs(u, v);

        tout[v] = time++;
    }

    ArrayList<Integer> merge(ArrayList<Integer> l1, ArrayList<Integer> l2) {

        int cnt = 0;
        ArrayList<Integer> res = new ArrayList<>();

        int p1 = 0;
        int p2 = 0;

        while (cnt < 10 && (p1 < l1.size() || p2 < l2.size())) {

            if (p1 >= l1.size()) {
                res.add(l2.get(p2));
                p2++;
            }
            else
            if (p2 >= l2.size()) {
                res.add(l1.get(p1));
                p1++;
            }
            else {

                if (l1.get(p1) == l2.get(p2)) {

                    res.add(l2.get(p2));
                    p1++;
                    p2++;
                }
                else
                if (l1.get(p1) > l2.get(p2)) {

                    res.add(l2.get(p2));
                    p2++;
                }
                else {

                    res.add(l1.get(p1));
                    p1++;
                }
            }

            cnt++;
        }

        return res;
    }

    long gcd(long a, long b) {

        if (b == 0)
            return a;

        return gcd(b, a%b);

    }

    class Pair implements Comparable<Pair>{

        int a;
        int b;

        Pair(int a, int b) {

            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {

            if (a < p.a)
                return -1;

            if (a > p.a)
                return 1;

            if  (b < p.b)
                return -1;

            if (b > p.b)
                return 1;

            return 0;
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

    }

}